The New World Translation study bible's Commentary on Acts ch.20:28

  the blood of his own Son: Lit., “through the blood of the own (one).” Grammatically, the Greek expression could be translated “with the blood of his own” or “with his own blood,” so the context has to be taken into consideration. In Greek, the expression ho iʹdi·os (“his own”) could stand alone without a clarifying noun or pronoun, as seen by how it is rendered at Joh 1:11 (“his own home”); at Joh 13:1 (“his own”); at Ac 4:23 (“their own people”); and at Ac 24:23 (“his people”). In non-Biblical Greek papyri, the phrase is used as a term of endearment to refer to close relatives. A reader of this verse would logically understand from the context that a noun in the singular number is implied after the expression “his own” and that the noun referred to God’s only-begotten Son, Jesus Christ, whose blood was shed. Based on this, quite a number of scholars and translators acknowledge that the word “son” is to be understood here and render the phrase “with the blood of his own Son.”

Acts ch.20:28 Contemporary English Version "Look after yourselves and everyone the Holy Spirit has placed in your care. Be like shepherds to God's church. It is the flock he bought with the blood of his own Son.+"

Acts ch.20:28Good News Translation"So keep watch over yourselves and over all the flock which the Holy Spirit has placed in your care. Be shepherds of the church of God,+ which he made his own through the blood of his Son.+"

Acts ch.20:28American Standard Version,"Take heed unto yourselves, and to all the flock, in which the Holy Spirit hath made you bishops, to feed the church of the Lord which he purchased with his own blood."

Acts ch.20:28Darby Bible Translation"Take heed therefore to yourselves, and to all the flock, wherein the Holy Spirit has set you as overseers, to shepherd the assembly of God, which he has purchased with the blood of his own. "

Acts ch.20:28New English Translation"Watch out for yourselves and for all the flock of which the Holy Spirit has made you overseers, to shepherd the church of God that he obtained with the blood of his own Son. "